Vol.4, No.7, 508-515 (2012)
http://dx.doi.org/10.4236/ns.2012.47068
Natural Science
Tropical cyclone, as powerful natural self-oscillatory
systems, and wind-energetic a way of struggle
against it
——The analysis of a cyclone from a position of the theory of vibrations
Kaganov William Ilich
Moscow State Institute of Radio Electronics and Automatics (MIREA), Moscow, Russia; [email protected]
Received 22 September 2011; revised 24 October 2011; accepted 10 November 2011
ABSTRACT
It is considered three phases of development of
a tropical cyclone: the origin, the steady-state
regime and the termination, coinciding with three
phases of self-oscillatory process: oscillation
buid-up, dynamic balance and failure of selfoscillations. The rough size of energy of a cyclone, as column of air rotating with high speed,
at initial and final stages of development and
comparison of the received sizes with nuclear
and hydrogen bombs is calculated. The model of
the electronic oscillator with negative active
conductivity by the numerical solution of the
equation of the Van-der-Pol is analyzed. Formal
coincidence of transient in this model with increase of capacity of vortical air formation, that
allows to make mnemonic model of a cyclone in
the form of volume self-oscillatory system is
shown. The numerical solution of the made
equations allows to construct schedules of dynamic process for each of particles of the investigated environment. The general recipe on restraint of development of a cyclone by compulsory entering into it of attenuation is given. Realization of this recipe by means of group of
platforms with powerful wind-electrogenerator
and the fans and uses of a principle of negative
feedback is shown. The results of laboratory
experiment confirming idea, taken as a principle
struggle against an arising air whirlwind, by
transformation of a laminar stream in chaotic,
turbulent are resulted. For fuller check offered a
wind-energetic method of struggle against a
cyclone carrying out of more scale experiment is
necessary.
Keywords: Tropical Cyclone; Model;
Copyright © 2012 SciRes.
Self-Oscillations; Wind Electrogenerator; The Fan;
Negative Feedback
1. THEORY
1.1. Essence of a Problem
The cyclones periodically arising in a tropical zone of
the Earth, possess enormous energy, comparable with
energy of a nuclear bomb at an origin stage, and hydrogen—after full formation. Cyclone action leads to numerous human victims and huge destructions. So, for
example, only the cyclone of “Katrina” operating in
North Atlantic pool in 2005, has caused the USA an
economic damage at the rate about 90 billion dollars. All
attempts to bridle or at least to reduce destructive force
of a cyclone haven’t crowned yet success. We will make
attempt to offer for the decision of the given global
problem one of branches of renewed electric power industry—wind. We will ask a question: whether it is impossible to stop by means of group of powerful wind
electrogenerators development of a tropical cyclone at
the initial stage of its origin? We will consider at first that
represents a cyclone as powerful natural power formation.
1.2. Three Phases of Development of a
Tropical Cylone
The phase 1 is connected with origin of the cyclone
representing atmospheric formation with lowered pressure of air in the center and with air streams, twirled in a
spiral with speed of a wind more than 17 km/s (Figure 1)
[1,2]. There is such cyclonic whirlwind over tropical
water area of ocean in temperature 26˚C - 27˚C at latitude between 50˚ and 20˚. The heated-up air sated with a
moisture, rising from an ocean surface on the big height,
it is cooled, owing to what water steams are condensed,
allocating heat feeding with energy arising cyclone.
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K. W. Ilich / Natural Science 4 (2012) 508-515
509
the further increase in the sizes of cyclonic formation
stops.
The phase 3 is connected with cyclone destruction
when total energy of all losses (cooling at the expense of
ocean, the friction about a terrestrial surface, overcoming
of obstacles) starts to surpass thermal energy, feeding
vortical air formation.
Having presented a cyclone in the form of a rotating
column of air (Figure 3), we will estimate its energy.
Weight of the cyclone:
H
m   π R 2   h  dh ,
(2)
0
where H—cyclone height, m; R—radius of the cyclone,
m; (h)—the density of air decreasing with height h at a
normal state from (0) = 1225 kg/m3.
Considering an ascending stream of air, we will accept
 = 0.8 kg/m3 = const at any value of height. Then kinetic energy of a rotating column of air:
W  0.25π HR 2V 2 ,
(3)
where V (km/s)—speed of a wind on cyclone periphery,
R (m)—radius a rotating column of air.
Having accepted for an arising cyclone V = 13 m/s, H
= 10 km and R = 10 km, we will receive according to (3)
for energy: W = 1014 J. For the generated cyclone we will
accept: V = 27 m/s, H = 10 km and R = 150 km. In this
Figure 1. Photos of a tropical cyclone.
Approximate dependence of temperature of air T on
height over a surface of ocean with temperature 27˚C can
be described by means of the characteristic of falling
type from the negative derivative considering fall of
temperature on 0.50 on each 100 m of height:
T  27  0.005  h,
(1)
where h height in m.
The schedule of function (1) is constructed on Figure
2. In the bottom part of a cyclone there can be air moving
to the axis center. But the great bulk of air which has
arisen cyclonic formations, under the influence of terrestrial Coriolis force connected with rotation of the Earth,
starts to rotate round a quasivertical axis counter-clockwise in northern hemisphere and on hour—in southern.
The phase 2 includes the gradual development of a
cyclone connected first of all with increase to 150 km
and more of radius rotating with high speed to 40 - 50
km/s of a column of air in height from 2 to 20 km, surrounded in the weight concerning cold and motionless air.
Achievement finally a cyclone of the maximum energy
and an establishment of a condition of dynamic balance
between thermal energy of evaporation feeding a cyclone,
and cooling of ocean owing to hashing of its waters then
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Figure 2. Dependence of temperature of air on height.
R
Hot wave
H
Ocean
Figure 3. The schematical image of a cyclone in the form of a
rotating column of air.
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K. W. Ilich / Natural Science 4 (2012) 508-515
case we will receive: W = 1017 J. For comparison we will
specify that the energy allocated at explosion of a nuclear
bomb in a trinitrotoluene equivalent 20 Kt, makes 1014 J,
and hydrogen in 20 Mt –1017 J. From the resulted figures
it is visible that at a stage of origin of a tropical cyclone
its energy is comparable with energy of a nuclear bomb,
and on final—hydrogen.
From positions of physics the cyclone is the original
thermal car in which warmly, selected from ocean, it will
be transformed to kinetic energy of a rotating air whirlwind. Such transformation is possible thanks to reduction
of temperature of air with height, i.e. to negative value of
a derivative dT dh  0 (Figure 1), and to rotation of
the Earth.
From a position of the theory of vibrations the cyclone
—a rotating column of air round a vertical axis—can be
treated as volumetric self-oscillatory process with three
phases of the development, aspiring to a limiting cycle—
to an equilibrium state between the energy feeding a cyclone (evaporation thermal energy), and total energy of
all losses (cooling at the expense of ocean, a friction with
a surface, overcoming of obstacles etc.).
For comparison we will consider at first more simple
case of self-oscillatory process also connected with presence at object of the falling characteristic from a negative
derivative.
1.3. The Short Analysis of the Electronic
Oscillator with Negative Active
Conductivity
It is known two basic types of electronic oscillators:
with positive feedback and with negative active conductivity [3].
The block diagram of the second type of the oscillatory contour consisting of the power supply of a direct
current, oscillatory system and the device with negative
active conductivity it agree characteristic volt-ampernoj
(a site а-б), shown on Figure 4(a) it is resulted on Figure 4(b). Its work, as well as the first type of the oscillator, can be described by means of the equation of the
Van-der-field [3]:
I
a
d2 x
dx
 a1 1  a2 x 2
 x  0,
dt
dt 2


(4)
where x—нормированная amplitude of fluctuations.
The numerical decision of the Eq.4 under the program
in the environment of Mathcad (The Appendix 1) is possible at almost any values of constant factors а1 and а2.
The example of the decision of the given equation at а1 =
0.1 and а2 = 0.5,  = 0, A = 10 B = 0 in the form of the
transient schedule x(t) and a phase portrait dx/dt = Ф(x)
with a limiting steady cycle is shown on Figure 5. Process includes sites of gradual increase of fluctuations and
the established mode with constant amplitude. For failure
of self-oscillations in system it is necessary to bring in it
attenuation. Let this attenuation is brought by means of
the external influence described by function F(t) =
Aexp(–t) – B. Then we will receive the following modified equation of the Van-der-field describing work of the
oscillator:
d2 x
dx
 a1  A exp   t   B   a2 x 2  exp   t   x  0 .
dt 2
dt
(5)
The decision of the Eq.6 under the program resulted in
Application 1, at а1 = 0.05, а2 = 0.5,  = 0.05, A = 10, B
= 1 in the form of the schedules similar to first case, it is
shown on Figure 6. Thanks to entering into the oscillator
of additional losses of fluctuation after achievement of
some maximum fade. This process of increase and the
further attenuation of self-oscillations is visually traced
and on a phase portrait: at first fluctuations aspire to a
limiting cycle, and then they start to be braided, aspiring
to the center. Thus, in this case process of self-oscillations instead of two has all three described above a phase:
increase of fluctuations, dynamic balance and failure of
self-oscillations.
1.4. Mnemonic Model of a Tropical Cyclone
Making a start from the Eq.5, we will make mathematical model of the tropical cyclone considered as
self-oscillatory system of volume type in rectangular
dI/dU 0
Direct current
source
b
U
(a)
The electronic
device
Oscilator contour
(b)
Figure 4. The oscillator with negative active conductivity: (a) Volt-ampernaja the characteristic; (b) The block diagram.
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K. W. Ilich / Natural Science 4 (2012) 508-515
(a)
511
(b)
Figure 5. Transient (a) and a phase portrait of the oscillator (b).
(a)
(b)
Figure 6. Transient (a) and a phase portrait (b) the oscillator with compulsory attenuation.
system of coordinates at spiral character of movement of
air:

d2 x
dx
 a1 1  a2 x 2 exp   t    x  0 , 
2
dt
dt


d2 y
dy
2
 a3 1  a4 y exp    t   y  0, 
2
dt
dt

z   t,







(6)
According to the assumptions accepted in aerohydrodynamics of the Eq.6 reflect dynamic process for each of
particles of the investigated environment. We will solve
system of the Eq.6 numerical way under the program by
means of a method of Runge-Kutta of 4th order in
mathematical Mathcad environment (The Application 2).
The schedules received as a result of calculation under
the program in the absence of external braking influence
on system (factors α = 0, β = 0, A = 1, B = 0) and value
of factors а1 = 0.2, а2 = 0.02, а3 = 0.2, а4 = 0.02,  = 2, Ω
= 1.01 are resulted Figure 7. On schedules it is accurately looked through spiral character of development of
the process, a tropical cyclone reminding under the form.
The analysis of the Eq.7 shows what to stop development of self-oscillatory process of volume type it is possible, as well as at the analysis of this process on a plane,
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by gradual entering into system of additional losses. By
analogy to the Eqs.5 and 6 mathematical models of a
cyclone in this case will become:
d2 x
dx
 a1  A exp   t   B   a2 x 2   x  0 ,
2
dt
dt
2
d y
dy
 a3  A exp    t   B   a4 y 2   y  0 ,
dt
dt 2
z   t,




 (7)




where factors α > 0 and β > 0.
The example of the decision of the Eq.7 at values of
factors а1 = 0.1, а2 = 0.5, а3 = 0.1, а4 = 0.5, α = 0.05, β =
0.05,  = 2, Ω = 1.05, A = 10, B = 1 is resulted on Figure
8. In this case, as well as in an example shown on Figure
6, process of self-oscillations instead of two has all three
described above a phase: increase of fluctuations, dynamic balance and failure of self-oscillations.
1.5. Vetroenergetichesky Way of Entering of
Attenuation in Self-Oscillatory Process
The Eq.7 gives the general recipe on restriction of development of self-oscillatory process in system by entering into it of compulsory losses, but, naturally, don’t
answer a question as practically it can be carried out.
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K. W. Ilich / Natural Science 4 (2012) 508-515
(a)
(c)
(b)
(d)
Figure 7. Transient (a); A phase portrait (b); Two-dimensional (c) and three-dimensional (d) the image of model of
a cyclone.
(a)
(c)
(b)
(d)
Figure 8. Transient (a, b); Two-dimensional (c) and three-dimensional (d) the image of model of a cyclone of type
with compulsory attenuation.
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Let’s consider thereupon platform work on which one
end it is established powerful wind generator, and on
another—the fan. At the analysis of work of the wind
electrogenerator it is necessary to consider three kinds of
transformation of energy and accordingly three kinds of
capacity: kinetic energy in unit of time an air stream with
a speed V; mechanical energy of a rotating propeller or
the turbine and electric energy of the wind electrogenerator. Thus capacity PG  V3. Considering a great speed
of a cyclonic wind, capacity а wind electrogenerator it is
possible to accept equal PG = 1 Gw. Such capacity has,
for example, with the wind electrogenerator the turbine
of the vertical type, developed by firm MWTT from
Arigony. The received electric energy is used for an electric motor food on which axis the propeller or the turbine
is established. At the efficiency equal of 50%, the work
made by such fan:
WG  0.5 PG ТW  0.5  109 ТW  J  ,
(8)
where TW—a fan operating time in s.
Similar group of the wind generators-fans established
on a platform, it is necessary to place on cyclone periphery (Figure 9). Propellers of fans should rotate clockwise,
i.e. in a direction opposite to rotation of a vortical air
stream in northern hemisphere that should promote
braking of development of a cyclone. Thus, in considered
model the part of kinetic energy of a cyclone at first will
be transformed to electric energy of group of wind electrogenerators which then turns to the energy injected by
means of fans in the form of local directed air streams in
the basic, “parent” stream in an opposite direction from it
and consequently braking development of last. Such
power system with negative feedback on energy can be
presented in the form of the block diagram resulted on
Figure 10. First of all two parameters estimate work of
the given system: the relation of the “organized” energy
WG thrown in the basic air stream by fans, to kinetic
513
Kinetic energy of
cyclone WC
The energy injected in a
cyclone WG
The energy selected
from a cyclone
Figure 10. The block diagram of a power system with negative
feedback.
energy of “parent” stream WC, Т.Е a cyclone. We name
the given relation in power factor of feedback k =
WG WC .
The second parameter characterizes the inertial properties of the system connected with time of a raising of
heated-up air sated moisture from a surface of ocean till
the moment of condensation of water steams and allocation by them of heat, feeding with energy a cyclone. At
vertical speed of a raising of air V = 1 m/s and height on
which there is a condensation of steams, in 5 - 10 km, we
will receive for given time ТC = 5000 - 10,000s. During
ТC fans should inject such quantity of the “organized”
energy which its development should start to brake into a
cyclone. Parameters k and ТC define values of factors α >
0 and β > 0 in the Eq.8.
The physical mechanism of possible prevention of
development of a tropical cyclone at the initial stage
when its development can be stopped by means of group
of wind generators-fans is that in general. The last can be
placed by the special high-speed ships operated by radio
and directed to a zone of origin of cyclonic formation
after its detection by means of meteorological companions.
2. LABORATORY EXPERIMENT
Platform with the
wind generator
and the fan
Cyclonic
whirlwind
Figure 9. The platforms which had on periphery of a cyclone.
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For check of working capacity of the idea taken as a
principle offered way of struggle against the arising cyclone, the following experiment has been made. At the
bottom of a cylindrical vessel in diameter of 25 sm and
height 40 sm the fan creating a vortical air stream
counter-clockwise (cyclone imitation) in 0.05 has been
placed m3/s. Over this fan four small fans rotating
clockwise, with total capacity of wind streams nearby
0.005 m3/s (Figure 11) have been placed. At the bottom
of a vessel the water which is warmed up from below to
temperature of boiling and production of steam is poured.
At inclusion only the big fan in a vessel the cyclic stream
of laminar type of warmed up air was formed. At simultaneous inclusion of all five fans the laminar stream was
transformed to the turbulent. For the best super-vision
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K. W. Ilich / Natural Science 4 (2012) 508-515
The small fan
The big fan
Heating
Figure 11. The laboratory installation modeling destruction of a
cyclone.
over process of transformation of a laminar stream of air
in turbulent in water the metal iodine giving to steams
pink coloring has been dissolved.
Thus, the made laboratory experiment has confirmed
idea of possible braking of powerful vortical cyclic process by means of other specially organized streams twirled
in the opposite side. According to experiment value of
factor k = 0.1.
Let’s in passing notice that usually try to get rid from
turbulent, whirl of gas and a liquid, creating additional
losses and to keep the laminar, ordered process of movement. The opposite recipe here is offered: a laminar
stream to transform in chaotic, turbulent which will interfere with cyclone development.
clone at the initial stage of its origin it is possible to accept factor k = 0.1, and for calculation of energy of fans
time TW = 2000с < TC. As a result for energy of one fan
at its capacity in 0.5 Gw it agree (8) we will receive: WG
≈ 1012 J. Hence, at energy of a cyclone at initial stage WC
= 1014 J and factor k = 0.1 for its destruction 10 generators-fans is required.
4. THE CONCLUSIONS
From the spent analysis and laboratory experiment
such conclusions follow:
 The energy destroying a cyclone, should be comparable to its kinetic energy, roughly 1:10, therefore to
brake the cyclone it is necessary at the initial stage of
its origin;
 Energy of braking as the source should use a cyclone
by direct selection from it parts of energy with the
help wind electrogenerator and transformations of
their electric energy to air streams by means of powerful fans; at the heart of such transformation the
principle of negative feedback consisting in this case
in injection in a cyclone of additional energy in an
opposite direction from the basic movement lies;
 It is necessary to transform the ordered, air streams
rotating on a spiral in chaotic, turbulent which won’t
allow to a cyclone to develop free;
 For full check of the offered idea on cyclone destruction at the initial stage of its development more fullscale experiment in pool in diameter more 50 m is
required.
REFERENCES
3. QUANTITATIVE ESTIMATION OF
PARAMETERS OF WORKING
SYSTEM
[1]
Pogosjan, H.P. (1976) Cyclone’s. Meteo Publisher.
[2]
Kachurin, L.G. (1978) Physical of a basis of influence on
atmospheric processes. Meteo Publisher.
From resulted above the data follows that for the
worker wind-energetic systems of destruction of a cy-
[3]
Kaganov, V.I. (2005) Radio engineering chains and signals. The computerized course. Forum Publisher.
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K. W. Ilich / Natural Science 4 (2012) 508-515
515
APPENDIX 1
ORIGIN : 1
 0.05 
 0 
a : 
y :    : 0.05
A : 10 B : 1

 0.5 
 0.2 
y2



F  t , y  : 
2
 a1   A  exp  a  t   B  a2  y1   y2  y1 


Z : rkfixed  y, 0, 400, 2001, F 
t : Z
1
x : Z
2
dx : Z
3
APPENDIX 2
ORIGIN : 1
 0
 
1
y :  
 2 
 
1
 0.1 
 
0.5
a :  
 0.1 
 
 0.5 
N : 1001 TK : 100  : 1.05
A : 10 B : 1
 : 0.05  : 0.05  : 2
y3




y4


F  t , y  :  a   A  exp  a  t   B  a  y 2  y    y 
2
1
1
 1 
 3


2
 a3   A  exp   a  t   B   a4  y2   y4  y2 
ZK : Rkadapt  y, 0, TK , N , F 
t : ZK
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1
X : ZK
2
Y : ZK
3
Z : ZK
1
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